So if I put something classified into an email and send it to you can the FBI throw you in jail?
It depends. If you know (or suspect) the information is classified (marked or not), AND you don't report it to your security manager, AND/OR you disclose that information to someone who isn't cleared AND has no need to know, then YES, you can be thrown in jail.
There have been classified documents read into the Congressional record by members of Congress. Nothing happened to the Congress-critters, because they have immunity for anything they say on the floor of their chamber.
There have also been classified documents posted to the Internet (WikiLeaks, etc.). If you have a clearance, and you know the information you're viewing online is classified, you are violating your NDA. You have no need to know, and for all you know, the information is DISinformation -- intended to catch government employees of guard or plant seeds of doubt in their minds about their loyalty to the government.
When WikiLeaks published the Clinton emails, everyone with a clearance was warned to stay away. Even though the information is now in the public domain, it's still classified unless someone declassifies it. You are still bound by the handing rules for classified info. Joe Blow with no clearance can copy and paste it into emails, but you'll be guilty of violating the law.